Pricing multivariate european equity option using gaussian mixture distributions and evt-based copulas

TL;DR

This paper introduces a novel approach for pricing multivariate European equity options by incorporating extreme value effects through Gaussian mixture models for marginals and EVT-based copulas for dependence, applied to CAC40 stocks.

Contribution

It presents a new method combining Gaussian mixture distributions and EVT-based copulas to better model extreme events in equity option pricing.

Findings

Effective modeling of extreme returns improves option valuation accuracy.

Application to CAC40 stocks demonstrates practical viability.

Monte Carlo simulations validate the approach.

Abstract

In this article, we present an approach which allows to take into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associeted options. Specifically, the marginal distribution of assets returns is modeled by a mixture of two gaussiens distributions. Moreover, we model the joint dependence structure of the returns using an extremal copula which is suitable for our financial data. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte-Carlo method is used to compute the values of some equity options: the call on maximum, the call on minimum, the digital option and the spreads option with the basket (Atos, Dassault systems).